document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=250727>Question 250727</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am a little lost at graphing linear equations. could you explain to me the whole concept of how to graph a linear equation? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #182608 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=182608\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you have two points on the line, then just plot them and draw a line through them. Otherwise...<ol><li>Find a point on the line. Any point will work but some are better than others. (If (-143, 2035) is a point on the line it will not be convenient to use it.) Often the y-intercept is used. Just pick a value for x and use that value and the equation to find the y for that x.</li><li>Plot the point on the graph.</li><li>Find the slope of the line. There are several common ways of finding the slope of a line:<ul><li>If the equation is in (or has been transformed into) slope-intercept form, y = mx + b, the slope is the coefficient of x. (Note: This form is also useful for finding the y-intercept which can be used for the point in steps #1 and #2.)</li><li>If the equation is in (or has been transformed into) Standard form, Ax + By = c, then the slope is -A/B.</li><li>Find a second point on the line and use the slope formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li></ul></li><li>If the slope is not a fraction, write it as a fraction. Any fraction equal to the slope will work. For example, if the slope is 2 we could use any of these: 2/1, 4/2, 6/3, -2/-1, etc.</li><li>Starting from the point you graphed at step #2:<ul><li>go up or down based on the numerator of the slope</li><li>go right or left based on the denominator of the slope</li><li> and plot a point where you end up.</li></ul></li><li>Use a ruler and draw a line through the two points.</li></ol><BR>\n" );
document.write( "Here's a simple example: To graph the equation y = -3x + 1...<BR>\n" );
document.write( "1) Find a point on the line. Since this equation is in slope-intercept form we can simply \"read\" the y-intercept of 1.<BR>\n" );
document.write( "2) Plot the point. Plot a point at 1 on the y-axis: (0, 1)<BR>\n" );
document.write( "3) Find the slope. We can also \"read\" the slope from the slope-intercept form: -3.<BR>\n" );
document.write( "4) Write the slope as a fraction. We can use -3/1.<BR>\n" );
document.write( "5) Starting from our plotted point (0, 1) we go down 3 (because the numerator of the slope is -3) and to the right by 1 (because the denominator of the slope fraction is 1). This should put us at (1, -2). Plot this point.<BR>\n" );
document.write( "6) Draw a line through the two points (0, 1) and (1, -2)<br><BR>\n" );
document.write( "If we use 3/-1 for the slope fraction instead of -3/1, we end up with the same line, believe it or not. We start from (0, 1) and go up 3 (because the numerator of the alternate slope fraction is 3) and go to the left by 1 (because the denominator of the alternate slope fraction is -1). This puts us at (-1, 4). Even though the two points we use are different, when we draw a line through each pair, we end up with the same line! </SPAN>\n" );
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